We get the number of nonnegative integer solution for the given pair of equations as 36 and 105 respectively.
The number of non-negative integer solutions of x1+x2+x3=7 is the number of permutations of a multiset with seven 1's, and two +'s. This is
9!/7!2! = 36
Similarly, the number of non-negative integer solutions of x4+x5+x6=13 is the number of permutations of thirteen 1's, and two +'s. This is
15!/13!2! = 105
This is why the first number in your combination is what the variables equal, and the second is "one less" the amount of variables, since you're permuting the +'s.
Hence we get the required answer.
Learn more about Permutations and combinations here:
brainly.com/question/11732255
#SPJ4
How many nonnegative integer solutions are there to the pair of equations x1+x2+…+x6=20 and x1+x2+x3=7?
